Paul Bunyan's Brachistochrone and Tautochrone
In this paper we concern ourselves with modified versions of the traditional brachistochrone and tautochrone problems. In the modified version of each problem the constant gravity model is replaced with an attractive inverse square law, consequently we name these the 1/{tau}{sup 2} brachistochrone and 1/{tau}{sup 2} tautochrone problems. With regard to the 1/{tau}{sup 2} brachistochrone problem, we show that the shape of the minimizing curve is formally constructed from an infinite series of elliptic integrals, and we use a numerical optimal control technique to generate the trajectories. The 1/{tau}{sup 2} tautochrone problem is solved using fraction calculus together with Lagrange's rule for tautochronous curves
- Research Organization:
- Sandia National Labs., Albuquerque, NM, and Livermore, CA (US)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 763091
- Report Number(s):
- SAND2000-2108J; TRN: AH200038%%281
- Journal Information:
- Journal of the Astronautical Sciences, Other Information: Submitted to Journal of the Astronautical Sciences; PBD: 21 Aug 2000
- Country of Publication:
- United States
- Language:
- English
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